Reachability Is NP-Complete Even for the Simplest Neural Networks

TL;DR

This paper proves that the reachability problem remains NP-complete even for very simple neural networks and restricted input/output specifications, correcting previous proof flaws.

Contribution

It establishes NP-completeness of reachability for simple neural networks and specifications, correcting earlier proof errors and extending the complexity results.

Findings

NP-hardness holds for one-layer neural networks

NP-hardness holds for minimal parameter requirements

Previous proof flaws are corrected

Abstract

We investigate the complexity of the reachability problem for (deep) neural networks: does it compute valid output given some valid input? It was recently claimed that the problem is NP-complete for general neural networks and conjunctive input/output specifications. We repair some flaws in the original upper and lower bound proofs. We then show that NP-hardness already holds for restricted classes of simple specifications and neural networks with just one layer, as well as neural networks with minimal requirements on the occurring parameters.